Kernel based simple regularized multiple criteria linear program for binary classification and regression

Handling data classification and regression problems through linear hyperplane is a naive and simple idea. In this paper, inspired by the idea of multiple criteria linear programs (MCLP) and multiple criteria quadratic programs (MCQP), we proposed a novel method for binary classification and regression problem. There are two main advantages for the proposed approach. One is that both of these two models guarantee the existence of feasible solutions when the model parameters were chosen properly. The other is that nonlinear patterns could be handled and captured by introducing kernel function into MCLP framework with a more natural way than previous work. Various classical approaches and datasets were evaluated in our experiments, and the result on both toy and real world data demonstrate the correctness and effectiveness of our proposed methods.